Q.15.4 (c)  Use the formula v=\sqrt{\frac{\gamma P}{\rho }} to explain why the speed of sound in air

(c) increases with humidity.

Answers (1)
S Sayak

 v=\sqrt{\frac{\gamma P}{\rho }}

As the humidity of air increases, the proportion of water molecules(M=18) increases and that of Oxygen(M=32) and Nitrogen(M=28) decreases thus reducing the density of air and as the speed of sound is inversely proportional to the square root of density of air, the speed will increase as the density increases and thus it increases with an increase in humidity.